Question

While hiking, Julia kicked a small rock off a ledge that was meters above a crevasse. y=-4.9t^2+9 Use the graph to determine when the rock will hit the bottom of the crevasse, 2 meters below ground level. Round your answer to the nearest tenth of a second.

The rock will hit the bottom of the crevasse in ____ seconds.

(1 point)
Responses

1.5
1.5

4.9
4.9

9
9

18

Answer 1

To find out when the rock hits the bottom of the crevasse, we need to set the function \( y = -4.9t^2 + 9 \) equal to \( -2 \) (since the bottom of the crevasse is 2 meters below ground level).

Setting up the equation:

\[
-4.9t^2 + 9 = -2
\]

Now, we can add 2 to both sides:

\[
-4.9t^2 + 11 = 0
\]

Next, we can isolate \( t^2 \):

\[
-4.9t^2 = -11
\]

Dividing by -4.9 gives:

\[
t^2 = \frac{11}{4.9}
\]

Calculating \( \frac{11}{4.9} \):

\[
t^2 \approx 2.2449
\]

Taking the square root of both sides:

\[
t \approx \sqrt{2.2449} \approx 1.5
\]

So, rounding to the nearest tenth of a second, the rock will hit the bottom of the crevasse in approximately **1.5 seconds**.

The answer is:
**1.5 seconds**.